Also the type of solver used will have an impact of the mesh in the near wall region, in particular the placement of the wall adjacent cells to ensure the near wall region is being effectively modelled.

Very true. But this Pic of mesh was taken from the one of the very good journal paper of 1980s on turbine simulation. This simulation was used to judge the quality of turbulence models. But looking at the mesh, I feel it is highly distorted and wake region is also not properly captured. Also mesh has high expansion ratio at boundaries.

So I was wondering, how one can asses turbulence model performance when mesh is not of high quality?

PS. I have no quality metrics available due to reason discussed above.